JEE Mains · Chemistry · STD 11 - 2. structure of atom
If \(\mathrm{a}_0\) is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength \((\lambda)\) of the electron present in the second orbit of hydrogen atom? [n : any integer]
- A \(\frac{8 \pi a_0}{n}\)
- B \(\frac{2 a_0}{n \pi}\)
- C \(\frac{4 \mathrm{n}}{\pi \mathrm{a}_0}\)
- D \(\frac{4 \pi a_0}{n}\)
Answer & Solution
Correct Answer
(A) \(\frac{8 \pi a_0}{n}\)
Step-by-step Solution
Detailed explanation
\(r_n=\frac{a_0 n^2}{z}\) Also, \(2 \pi \mathrm{r}_{\mathrm{n}}=\mathrm{n} \lambda\) Where \(\lambda\) is de-Broglie wavelength \(\frac{2 \pi \mathrm{a}_0 \mathrm{n}^2}{\mathrm{z}}=\mathrm{n} \lambda\) For second orbit of H -atom \(\lambda=\frac{8 \pi \mathrm{a}_0}{\mathrm{n}}\)
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